How do recommendation systems work? - algorithm

I've always been curious as to how these systems work. For example, how do netflix or Amazon determine what recommendations to make based on past purchases and/or ratings? Are there any algorithms to read up on?
Just so there's no misperceptions here, there's no practical reason for me asking. I'm just asking out of sheer curiosity.
(Also, if there's an existing question on this topic, point me to it. "Recommendations system" is a difficult term to search for.)

At it's most basic, most recommendation systems work by saying one of two things.
User-based recommendations:
If User A likes Items 1,2,3,4, and 5,
And User B likes Items 1,2,3, and 4
Then User B is quite likely to also like Item 5
Item-based recommendations:
If Users who purchase item 1 are also disproportionately likely to purchase item 2
And User A purchased item 1
Then User A will probably be interested in item 2
And here's a brain dump of algorithms you ought to know:
- Set similarity (Jaccard index & Tanimoto coefficient)
- n-Dimensional Euclidean distance
- k-means algorithm
- Support Vector Machines

This is such a commercially important application that Netflix introduced a $1 million prize for improving their recommendations by 10%.
After a couple of years people are getting close (I think they're up around 9% now) but it's hard for many, many reasons. Probably the biggest factor or the biggest initial improvement in the Netflix Prize was the use of a statistical technique called singular value decomposition.
I highly recommend you read If You Liked This, You’re Sure to Love That for an in-depth discussion of the Netflix Prize in particular and recommendation systems in general.
Basically though the principle of Amazon and so on is the same: they look for patterns. If someone bought the Star Wars Trilogy well there's a better than even chance they like Buffy the Vampire Slayer more than the average customer (purely made up example).

The O'Reilly book "Programming Collective Intelligence" has a nice chapter showing how it works. Very readable.
The code examples are all written in Python, but that's not a big problem.

GroupLens Research at the University of Minnesota studies recommender systems and generously shares their research and datasets.
Their research expands a bit each year and now considers specifics like online communities, social collaborative filtering, and the UI challenges in presenting complex data.

The Netflix algorithm for its recommendation system is actually a competitive endeavor in which programmers continue to compete to make gains in the accuracy of the system.
But in the most basic terms, a recommendation system would examine the choices of users who closely match another user's demographic/interest information.
So if you are a white male, 25 years old, from New York City, the recommendation system might try and bring you products purchased by other white males in the northeast United States in the age range of 21-30.
Edit: It should also be noted that the more information you have about your users, the more closely you can refine your algorithms to match what other people are doing to what may interest the user in question.

This is a classification problem - that is, the classification of users into groups of users who are likely to be interested in certain items.
Once classified into such a group, it is easy to examine the purchases/likes of other users in that group and recommend them.
Therefore, Bayesian Classification and neural networks (multilayer perceptrons, radial basis functions, support vector machines) are worth reading up on.

One technique is to group users into clusters and recommend products from other users in the same cluster.

There're mainly two types of recommender systems, which work differently:
1. Content-based.
These systems make recommendations based on characteristic information. This is information about the items (keywords, categories, etc.) and users (preferences, profiles, etc.).
2. Collaborative filtering.
These systems are based on user-item interactions. This is information such as ratings, number of purchases, likes, etc.
This article (published by the company I work at) provides an overview of the two systems, some practical examples, and suggests when it makes sense to implement them.

Ofcourse there is algorithms that will recommend you with prefered items. Different data mining techniques have been implemented for that. If you want more basic details on Recommender System then visit this blog. Here every basics has been covered to know about Recommender System.

Related

Which open-source recommendation system should I choose to deal with big dataset

I want to build a recommendation system, and the target is to deal with really big data set, like 1 TB data.
And each user has really huge amount of items, however the number of user is small, like thousands or 10 thousands.
I have search from google, I found there is some open-source recommendation engine based on hadoop like Mahout, I guess it may have ability to deal with such big data, however I'm not sure.
I also find some engine write in C++ python, even php, I don't think script languages can deal with such big data, cause memory can't contain the whole dataset.
Or I'm wrong? Could some give me some recommendation?
Your question title is:
Which opensource recommendation system should I choose to deal with
big dataset?
and in the first line you say
I want to build a recommendation system, and the target is to deal with really big data set, > like 1 TB data.
And you are asking for an recommendation as an answer.
To answer your second question first. In my experience of building recommender systems I would advise you do not "build" a recommender system from the ground up if you can avoid it. Recommender Systems are complex and can use a wide range of techniques to provide a user with a recommendation. So my recommendation is unless you are really committed, and have a team of people with a range of experience and knowledge in recommender systems, statistics, and software engineering then look to implement an existing recommender system rather than building your own.
In terms of which open source recommender system you should choose, this is actually pretty difficult to answer with great accuracy. Let me try to answer this by breaking it down.
Consider the open source license, its restrictions and your requirements.
Consider which algorithm you want to use to make recommendations
Consider the environment you will be running your recommender system on.
I recommend you look more into the algorithm side as it will be the determining factor as to which tool you can use, or whether you will need to roll your own. Start reading here http://www.ibm.com/developerworks/library/os-recommender1/ for a very brief insight in to the different approaches that recommender systems use. In summary the different approaches are:
Content based
Neighbourhood / Collaborative filtering based
Constraint based
Graph-based
In your case to keep things relatively straightforward it sounds like you should consider a user-user collaborative filtering algorithm for this. The reasons being:
Neighbourhood Collaborative Filtering is quite intuitive to understand and it can be relatively easy to implement.
With this method you can also justify your recommendations to your users in a basic way
There is no requirement to build a model for training, and the processing of neighbours can be done "offline", to provide quick recommendations to the end user.
Storing neighbours is actually quite memory efficient, which means better scalability. Something it sounds like you will need lots of.
The user-based part of my suggestion is because it sounds like you have less users than you do items. In a user-based nearest neighbourhood a predicted rating of a new item I for user U is calculated by looking at the other users who have also rated item I and are most similar to user U. Because you have fewer users than items in your system it will be faster to compute user-based collaborative filtering compared with item-based collaborative filtering.
Within the user-based collaborative filtering you need to consider what rating normalisation (mean-centering vs z-score) you want to use, the similarity weight computation method (e.g. Cosine vs Pearsons correlation vs other similarity measures) you want to use, neighbourhood selection criteria (pre-filtering of neighbours, number of neighbours involved in the prediction), and any Dimensionality Reduction methods (SVD, SVD++) you want to implement (with a large dataset like yours you will want to seriously consider DM).
So really instead of looking for an open source that will be able to process your data set you should consider your algorithm choice first, then look to find a tool that has an implementation of this algorithm, and then assess whether it can process your the volume involved in your dataset.
In saying all of that, if you do choose to go down the user-based collaborative filtering route then I am confident that Apache Mahout will be able to solve your problem, and if not it will certainly help you understand the complexity involved in building your own (just look at their source code).
Please note the advice is really consider the algorithm choice. "Good" recommender systems are so much more than just being able to process a large dataset. You need to think about accuracy, coverage, confidence, novelty, serendipity, diversity, robustness, privacy, risk user trust, and finally scalability. You should also consider how you are going to perform experiments and evaluate your recommendations, remember if the recommendations you are churning out are rubbish and it is turning your users off then there is no point to have a recommender system!
It is such a big area with lots to think about, there is probably no one single tool that is going to help you with everything, so be prepared to do a lot of reading and research as well as implementing lots of different open source tools to help you.
In saying that, start looking at Apache Mahout. Going back to the break-down of the 3 areas I said you should think about.
It has a commercial-friendly open-source license,
it has really great implementation of the algorithms you are likely going to need to use, and
it can work on distributed environments (read scalable).
Hope that helps, and good luck.

Beyond item-to-item recommendations

Simple item-to-item recommendation systems are well-known and frequently implemented. An example is the Slope One algorithm. This is fine if the user hasn't rated many items yet, but once they have, I want to offer more finely-grained recommendations. Let's take a music recommendation system as an example, since they are quite popular. If a user is viewing a piece by Mozart, a suggestion for another Mozart piece or Beethoven might be given. But if the user has made many ratings on classical music, we might be able to make a correlation between the items and see that the user dislikes vocals or certain instruments. I'm assuming this would be a two-part process, first part is to find correlations between each users' ratings, the second would be to build the recommendation matrix from these extra data. So the question is, are they any open-source implementations or papers that can be used for each of these steps?
Taste may have something useful. It's moved to the Mahout project:
http://taste.sourceforge.net/
In general, the idea is that given a user's past preferences, you want to predict what they'll select next and recommend it. You build a machine-learning model in which the inputs are what a user has picked in the past and the attributes of each pick. The output is the item(s) they'll pick. You create training data by holding back some of their choices, and using their history to predict the data you held back.
Lots of different machine learning models you can use. Decision trees are common.
One answer is that any recommender system ought to have some of the properties you describe. Initially, recommendations aren't so good and are all over the place. As it learns tastes, the recommendations will come from the area the user likes.
But, the collaborative filtering process you describe is fundamentally not trying to solve the problem you are trying to solve. It is based on user ratings, and two songs aren't rated similarly because they are similar songs -- they're rated similarly just because similar people like them.
What you really need is to define your notion of song-song similarity. Is it based on how the song sounds? the composer? Because it sounds like the notion is not based on ratings, actually. That is 80% of the problem you are trying to solve.
I think the question you are really answering is, what items are most similar to a given item? Given your item similarity, that's an easier problem than recommendation.
Mahout can help with all of these things, except song-song similarity based on its audio -- or at least provide a start and framework for your solution.
There are two techniques that I can think of:
Train a feed-forward artificial neural net using Backpropagation or one of it's successors (e.g. Resilient Propagation).
Use version space learning. This starts with the most general and the most specific hypotheses about what the user likes and narrows them down when new examples are integrated. You can use a hierarchy of terms to describe concepts.
Common characteristics of these methods are:
You need a different function for
each user. This pretty much rules
out efficient database queries when
searching for recommendations.
The function can be updated on the fly
when the user votes for an item.
The dimensions along which you classify
the input data (e.g. has vocals, beats
per minute, musical scales,
whatever) are very critical to the
quality of the classification.
Please note that these suggestions come from university courses in knowledge based systems and artificial neural nets, not from practical experience.

How the computer knows "Recommended for You"?

Recently, I found several web site have something like : "Recommended for You", for example youtube, or facebook, the web site can study my using behavior, and recommend some content for me... ...I would like to know how they analysis this information? Is there any Algorithm to do so? Thank you.
Amazon and Netflix (among others) use a technique called Collaborative filtering to suggest things you might like based on the likes/dislikes of others who have made purchases and selections similar to yours.
Is there any Algorithm to do so?
Yes
Yes. One fairly common one is to look at things you've selected in the past, find other people who've made those selections, then find the other selections most common among those other people, and guess that you're likely to be interested in those as well.
Yup there are lots of algorithms. Things such as k-nearest neighbor: http://en.wikipedia.org/wiki/K-nearest_neighbor_algorithm.
Here is a pretty good book on the subject that covers making these sorts of systems along with others: http://www.amazon.com/gp/product/0596529325?ie=UTF8&tag=ianburriscom-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=0596529325.
It's generally done by matching you with other users who have similar usage history / profile and then recommending other things that they've purhased/watched/whatever.
Searching for "recommendation algorithm" yields lots of papers. Most algorithms incorporate "machine learning" algorithms to determine groups of things (comedy movies, books on gardening, orchestral music, etc.). Your matching with those groups yields recommendations. Some companies use humans to classify things, too.
Such an algorithm is going to vary wildly from company to company. In many cases, it analyzes some combination of your search history, purchase history, physical location, and other factors. It probably will also compare purchases/searches amongst other people to find what those people have purchased/searched for, and recommend some of those products to you.
There are probably hundreds of these algorithms out there, but I doubt you can use any of them (that are actually good). Probably you are better off figuring it out yourself.
If you can categorize your contents (i.e. by tagging or content analysis), you can also categorize your users and their preferences.
For example: you have a video portal with 5 million videos .. 1 mio of them are tagged mostly red. If 80% of all videos watched by a user (who is defined by an IP, a persistent user account, ...) are tagged mostly red, you might want to recommend even more red videos to him. You might want to refine your recommendations by looking at his further actions: does he like your recommendations -- if so, why not give him even more, if not, try the second-best guess, maybe he's not looking for color, but for the background music ...
There's no absolute algorithm to do it, but all implementations will go into a similar direction. It's always basing on observing users, which scares me from time to time :-)
There's whole lot of algorithms tackling the issue: Wiki article. It's a Machine Learning domain problem. Computer's can be learned using two main techniques: classification and clustering. They require some datasets as input. If the dataset is informative (really holds some useful patterns) than those ML techniques can dig most of it.
Clustering could be best to use for this kind of problem. It's main usage is to find similarities among points in provided dataset. If the points are, e.g. your search history, they can be grouped together to form certain clusters. If Your search history closely relates to another, a hint can be given - picking links that are most similar to Your's.
The same comes with book recommendations - it's obvious what dataset they use: "Other people who bought this product also bought Product A, Product B,...". The key here is to match your profile to other's and use the most similar to recommend.
The computer retrieves information from the human brain with complex memory scan process, sorts it accordingly and outputs results based on what you have experienced in your life so far.

How does the Amazon Recommendation feature work?

What technology goes in behind the screens of Amazon recommendation technology? I believe that Amazon recommendation is currently the best in the market, but how do they provide us with such relevant recommendations?
Recently, we have been involved with similar recommendation kind of project, but would surely like to know about the in and outs of the Amazon recommendation technology from a technical standpoint.
Any inputs would be highly appreciated.
Update:
This patent explains how personalized recommendations are done but it is not very technical, and so it would be really nice if some insights could be provided.
From the comments of Dave, Affinity Analysis forms the basis for such kind of Recommendation Engines. Also here are some good reads on the Topic
Demystifying Market Basket Analysis
Market Basket Analysis
Affinity Analysis
Suggested Reading:
Data Mining: Concepts and Technique
It is both an art and a science. Typical fields of study revolve around market basket analysis (also called affinity analysis) which is a subset of the field of data mining. Typical components in such a system include identification of primary driver items and the identification of affinity items (accessory upsell, cross sell).
Keep in mind the data sources they have to mine...
Purchased shopping carts = real money from real people spent on real items = powerful data and a lot of it.
Items added to carts but abandoned.
Pricing experiments online (A/B testing, etc.) where they offer the same products at different prices and see the results
Packaging experiments (A/B testing, etc.) where they offer different products in different "bundles" or discount various pairings of items
Wishlists - what's on them specifically for you - and in aggregate it can be treated similarly to another stream of basket analysis data
Referral sites (identification of where you came in from can hint other items of interest)
Dwell times (how long before you click back and pick a different item)
Ratings by you or those in your social network/buying circles - if you rate things you like you get more of what you like and if you confirm with the "i already own it" button they create a very complete profile of you
Demographic information (your shipping address, etc.) - they know what is popular in your general area for your kids, yourself, your spouse, etc.
user segmentation = did you buy 3 books in separate months for a toddler? likely have a kid or more.. etc.
Direct marketing click through data - did you get an email from them and click through? They know which email it was and what you clicked through on and whether you bought it as a result.
Click paths in session - what did you view regardless of whether it went in your cart
Number of times viewed an item before final purchase
If you're dealing with a brick and mortar store they might have your physical purchase history to go off of as well (i.e. toys r us or something that is online and also a physical store)
etc. etc. etc.
Luckily people behave similarly in aggregate so the more they know about the buying population at large the better they know what will and won't sell and with every transaction and every rating/wishlist add/browse they know how to more personally tailor recommendations. Keep in mind this is likely only a small sample of the full set of influences of what ends up in recommendations, etc.
Now I have no inside knowledge of how Amazon does business (never worked there) and all I'm doing is talking about classical approaches to the problem of online commerce - I used to be the PM who worked on data mining and analytics for the Microsoft product called Commerce Server. We shipped in Commerce Server the tools that allowed people to build sites with similar capabilities.... but the bigger the sales volume the better the data the better the model - and Amazon is BIG. I can only imagine how fun it is to play with models with that much data in a commerce driven site. Now many of those algorithms (like the predictor that started out in commerce server) have moved on to live directly within Microsoft SQL.
The four big take-a-ways you should have are:
Amazon (or any retailer) is looking at aggregate data for tons of transactions and tons of people... this allows them to even recommend pretty well for anonymous users on their site.
Amazon (or any sophisticated retailer) is keeping track of behavior and purchases of anyone that is logged in and using that to further refine on top of the mass aggregate data.
Often there is a means of over riding the accumulated data and taking "editorial" control of suggestions for product managers of specific lines (like some person who owns the 'digital cameras' vertical or the 'romance novels' vertical or similar) where they truly are experts
There are often promotional deals (i.e. sony or panasonic or nikon or canon or sprint or verizon pays additional money to the retailer, or gives a better discount at larger quantities or other things in those lines) that will cause certain "suggestions" to rise to the top more often than others - there is always some reasonable business logic and business reason behind this targeted at making more on each transaction or reducing wholesale costs, etc.
In terms of actual implementation? Just about all large online systems boil down to some set of pipelines (or a filter pattern implementation or a workflow, etc. you call it what you will) that allow for a context to be evaluated by a series of modules that apply some form of business logic.
Typically a different pipeline would be associated with each separate task on the page - you might have one that does recommended "packages/upsells" (i.e. buy this with the item you're looking at) and one that does "alternatives" (i.e. buy this instead of the thing you're looking at) and another that pulls items most closely related from your wish list (by product category or similar).
The results of these pipelines are able to be placed on various parts of the page (above the scroll bar, below the scroll, on the left, on the right, different fonts, different size images, etc.) and tested to see which perform best. Since you're using nice easy to plug and play modules that define the business logic for these pipelines you end up with the moral equivalent of lego blocks that make it easy to pick and choose from the business logic you want applied when you build another pipeline which allows faster innovation, more experimentation, and in the end higher profits.
Did that help at all? Hope that give you a little bit of insight how this works in general for just about any ecommerce site - not just Amazon. Amazon (from talking to friends that have worked there) is very data driven and continually measures the effectiveness of it's user experience and the pricing, promotion, packaging, etc. - they are a very sophisticated retailer online and are likely at the leading edge of a lot of the algorithms they use to optimize profit - and those are likely proprietary secrets (you know like the formula to KFC's secret spices) and guaarded as such.
This isn't directly related to Amazon's recommendation system, but it might be helpful to study the methods used by people who competed in the Netflix Prize, a contest to develop a better recommendation system using Netflix user data. A lot of good information exists in their community about data mining techniques in general.
The team that won used a blend of the recommendations generated by a lot of different models/techniques. I know that some of the main methods used were principal component analysis, nearest neighbor methods, and neural networks. Here are some papers by the winning team:
R. Bell, Y. Koren, C. Volinsky, "The BellKor 2008 Solution to the Netflix Prize", (2008).
A. Töscher, M. Jahrer, “The BigChaos Solution to the Netflix Prize 2008", (2008).
A. Töscher, M. Jahrer, R. Legenstein, "Improved Neighborhood-Based Algorithms for Large-Scale Recommender Systems", SIGKDD Workshop on Large-Scale Recommender Systems and the Netflix Prize Competition (KDD’08) , ACM Press (2008).
Y. Koren, "The BellKor Solution to the Netflix Grand Prize", (2009).
A. Töscher, M. Jahrer, R. Bell, "The BigChaos Solution to the Netflix Grand Prize", (2009).
M. Piotte, M. Chabbert, "The Pragmatic Theory solution to the Netflix Grand Prize", (2009).
The 2008 papers are from the first year's Progress Prize. I recommend reading the earlier ones first because the later ones build upon the previous work.
I bumped on this paper today:
Amazon.com Recommendations: Item-to-Item Collaborative Filtering
Maybe it provides additional information.
(Disclamer: I used to work at Amazon, though I didn't work on the recommendations team.)
ewernli's answer should be the correct one -- the paper links to Amazon's original recommendation system, and from what I can tell (both from personal experience as an Amazon shopper and having worked on similar systems at other companies), very little has changed: at its core, Amazon's recommendation feature is still very heavily based on item-to-item collaborative filtering.
Just look at what form the recommendations take: on my front page, they're all either of the form "You viewed X...Customers who also viewed this also viewed...", or else a melange of items similar to things I've bought or viewed before. If I specifically go to my "Recommended for You" page, every item describes why it's recommended for me: "Recommended because you purchased...", "Recommended because you added X to your wishlist...", etc. This is a classic sign of item-to-item collaborative filtering.
So how does item-to-item collaborative filtering work? Basically, for each item, you build a "neighborhood" of related items (e.g., by looking at what items people have viewed together or what items people have bought together -- to determine similarity, you can use metrics like the Jaccard index; correlation is another possibility, though I suspect Amazon doesn't use ratings data very heavily). Then, whenever I view an item X or make a purchase Y, Amazon suggests me things in the same neighborhood as X or Y.
Some other approaches that Amazon could potentially use, but likely doesn't, are described here: http://blog.echen.me/2011/02/15/an-overview-of-item-to-item-collaborative-filtering-with-amazons-recommendation-system/
A lot of what Dave describes is almost certainly not done at Amazon. (Ratings by those in my social network? Nope, Amazon doesn't have any of my social data. This would be a massive privacy issue in any case, so it'd be tricky for Amazon to do even if they had that data: people don't want their friends to know what books or movies they're buying. Demographic information? Nope, nothing in the recommendations suggests they're looking at this. [Unlike Netflix, who does surface what other people in my area are watching.])
I don't have any knowledge of Amazon's algorithm specifically, but one component of such an algorithm would probably involve tracking groups of items frequently ordered together, and then using that data to recommend other items in the group when a customer purchases some subset of the group.
Another possibility would be to track the frequency of item B being ordered within N days after ordering item A, which could suggest a correlation.
As far I know, it's use Case-Based Reasoning as an engine for it.
You can see in this sources: here, here and here.
There are many sources in google searching for amazon and case-based reasoning.
If you want a hands-on tutorial (using open-source R) then you could do worse than going through this:
https://gist.github.com/yoshiki146/31d4a46c3d8e906c3cd24f425568d34e
It is a run-time optimised version of another piece of work:
http://www.salemmarafi.com/code/collaborative-filtering-r/
However, the variation of the code on the first link runs MUCH faster so I recommend using that (I found the only slow part of yoshiki146's code is the final routine which generates the recommendation at user level - it took about an hour with my data on my machine).
I adapted this code to work as a recommendation engine for the retailer I work for.
The algorithm used is - as others have said above - collaborative filtering. This method of CF calculates a cosine similarity matrix and then sorts by that similarity to find the 'nearest neighbour' for each element (music band in the example given, retail product in my application).
The resulting table can recommend a band/product based on another chosen band/product.
The next section of the code goes a step further with USER (or customer) based collaborative filtering.
The output of this is a large table with the top 100 bands/products recommended for a given user/customer
Someone did a presentation at our University on something similar last week, and referenced the Amazon recommendation system. I believe that it uses a form of K-Means Clustering to cluster people into their different buying habits. Hope this helps :)
Check this out too: Link and as HTML.

Algorithm for suggesting products

What's a good algorithm for suggesting things that someone might like based on their previous choices? (e.g. as popularised by Amazon to suggest books, and used in services like iRate Radio or YAPE where you get suggestions by rating items)
Simple and straightforward (order cart):
Keep a list of transactions in terms of what items were ordered together. For instance when someone buys a camcorder on Amazon, they also buy media for recording at the same time.
When deciding what is "suggested" on a given product page, look at all the orders where that product was ordered, count all the other items purchased at the same time, and then display the top 5 items that were most frequently purchased at the same time.
You can expand it from there based not only on orders, but what people searched for in sequence on the website, etc.
In terms of a rating system (ie, movie ratings):
It becomes more difficult when you throw in ratings. Rather than a discrete basket of items one has purchased, you have a customer history of item ratings.
At that point you're looking at data mining, and the complexity is tremendous.
A simple algorithm, though, isn't far from the above, but it takes a different form. Take the customer's highest rated items, and the lowest rated items, and find other customers with similar highest rated and lowest rated lists. You want to match them with others that have similar extreme likes and dislikes - if you focus on likes only, then when you suggest something they hate, you'll have given them a bad experience. In suggestions systems you always want to err on the side of "lukewarm" experience rather than "hate" because one bad experience will sour them from using the suggestions.
Suggest items in other's highest lists to the customer.
Consider looking at "What is a Good Recommendation Algorithm?" and its discussion on Hacker News.
There isn't a definitive answer and it's highly unlikely there is a standard algorithm for that.
How you do that heavily depends on the kind of data you want to relate and how it is organized. It depends on how you define "related" in the scope of your application.
Often the simplest thought produces good results. In the case of books, if you have a database with several attributes per book entry (say author, date, genre etc.) you can simply chose to suggest a random set of books from the same author, the same genre, similar titles and others like that.
However, you can always try more complicated stuff. Keeping a record of other users that required this "product" and suggest other "products" those users required in the past (product can be anything from a book, to a song to anything you can imagine). Something that most major sites that have a suggest function do (although they probably take in a lot of information, from product attributes to demographics, to best serve the client).
Or you can even resort to so called AI; neural networks can be constructed that take in all those are attributes of the product and try (based on previous observations) to relate it to others and update themselves.
A mix of any of those cases might work for you.
I would personally recommend thinking about how you want the algorithm to work and how to suggest related "products". Then, you can explore all the options: from simple to complicated and balance your needs.
Recommended products algorithms are huge business now a days. NetFlix for one is offering 100,000 for only minor increases in the accuracy of their algorithm.
As you have deduced by the answers so far, and indeed as you suggest, this is a large and complex topic. I can't give you an answer, at least nothing that hasn't already been said, but I an point you to a couple of excellent books on the topic:
Programming CI:
http://oreilly.com/catalog/9780596529321/
is a fairly gentle introduction with
samples in Python.
CI In Action:
http://www.manning.com/alag looks a
bit more in depth (but I've only just
read the first chapter or 2) and has
examples in Java.
I think doing a Google on Least Mean Square Regression (or something like that) might give you something to chew on.
I think most of the useful advice has already been suggested but I thought I'll just put in how I would go about it, just thinking though, since I haven't done anything like this.
First I Would find where in the application I will sample the data to be used, so If I have a store it will probably in the check out. Then I would save a relation between each item in the checkout cart.
now if a user goes to an items page I can count the number of relations from other items and pick for example the 5 items with the highest number of relation to the selected item.
I know its simple, and there are probably better ways.
But I hope it helps
Market basket analysis is the field of study you're looking for:
Microsoft offers two suitable algorithms with their Analysis server:
Microsoft Association Algorithm Microsoft Decision Trees Algorithm
Check out this msdn article for suggestions on how best to use Analysis Services to solve this problem.
link text
there is a recommendation platform created by amazon called Certona, you may find this useful, it is used by companies such as B&Q and Screwfix find more information at www.certona.com/‎

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